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Hi Peter,
What we naively refer to as the "Quantum Scale" is actually two self-similar scales: a Quantum and a Sub-Quantum. The implication of "sub-quantum" (which I compare with the Dirac Sea, and I think is the origin of mass) is that some of these "fundamental particles" that we observe at the Quantum Scale may actually be composite particles. I know that Technicolour is out of fashion because it hasn't been supported by experimental data (yet), but my paper in Prespacetime Journal, volume 1, issue 9, implies that gluons may behave like Cooper pairs of something more fundamental.
I know that Edwin Eugene Klingman has serious problems with QCD and its 5% (at best - after radiative corrections) accuracy. Perhaps we are incorrectly treating a Cooper pair quasiparticle like a fundamental particle (gluons). This could have significant implications regarding the use of the Partition Function and radiative corrections.
Your General Metric implies at least 16 dimensions. I am proposing that these dimensions are scattered over different scales, but that these different scaled dimensions twist together (like twistors, and perhaps because of the properties of Lucas numbers?) into effective quasi-dimensions that have this oddball nature of wave-particle duality (and the corresponding continuous-discrete duality) because our "dimensions" are actually composite. This allows a fractal reality (self-similar scales implies fractal) to appear discrete (we observe 3 spatial plus one temporal dimensions - not fractions of dimensions)because of Lucas Numbers: 1.618-0.618=1.000 TIME!, 2.618+0.388=3.000 SPACE!, etc.
Any particular measurement can only obtain - at most - half of the dynamic variables present (say momentum OR position), so pairs of twisted reciprocally-scaled dimensions (sounds a lot like Cooper pairs, but these Lucas numbers can have identical, even or odd symmetries) can behave like single quasi-dimensions.
Your analysis of the Planck units opens more questions than it answers. Suppose that each Scale has its own Planck Constant?
You said "Particles have discrete character and spacetime (= relativity) has a continuous character." I agree, and I am saying that this is caused by interacting Scales and twisted quasi-dimensions.
You asked "Do you think that the difference between the Probability Wave description (= continuous) and the description of particles (= discrete) is only a mathematical problem?" I think it is due to wave-particle duality, which is due to these twistor-like reciprocally-scaled dimensions.
I hope I answered your questions thoroughly enough. I look forward to seeing if your ideas reinspire mine, and/or vice versa.
Have Fun!
Dr. Cosmic Ray